Richard von Mises Lecture 2026

Abstract

From Simulation to Decision Intelligence: A Mathematical Roadmap for Scientific Machine Learning

Wil Schilders (TU Eindhoven · Hans Fischer senior fellow at TUM-IAS · ICIAM president)

Over the past decades, computational science has reached a remarkable level of maturity: in principle, we are able to simulate highly complex systems with great accuracy. Yet in practice, simulation remains underused where it matters most — namely in fast, real-world decision-making processes. This paradox reflects a fundamental gap between capability and usability: models are often too slow, too complex, and insufficiently robust to be integrated into modern workflows.

Scientific machine learning offers a promising route forward by combining data-driven approaches with classical modelling. However, current methods frequently lack the reliability, interpretability, and guarantees required for deployment in industrial and scientific settings. In this lecture, we argue that bridging this gap requires a shift from black-box learning to structure-aware modelling, in which mathematical principles, such as stability, model reduction, and the enforcement of physical laws, are embedded by design.

This perspective leads to an ambitious vision: simulation as a real-time, adaptive, and trustworthy component of decision-making, forming the backbone of emerging concepts such as digital twins. Realizing this vision will require mathematics not only to support, but to guide and shape the development of scientific machine learning, continuing the tradition of Richard von Mises, who viewed mathematics as an integral part of the scientific enterprise.